How this instrument works
Relative centrifugal force restates the centripetal acceleration inside a spinning rotor as a multiple of standard gravity, rather than in raw units of length over time squared. A point at radius r sweeping at angular speed ω feels acceleration ω²r; converting revolutions per minute to radians per second and dividing by standard gravity, g₀ = 9.80665 m/s², collapses the whole calculation into RCF = 1.118 × 10⁻⁵ · r · RPM², with r read directly in centimetres. The constant is not arbitrary — it is (2π/60)² divided by 100 and by g₀, folded into one figure so the formula accepts rotor radius and RPM straight off the equipment without a manual conversion step.
Because RPM enters the formula squared, doubling a rotor's speed quadruples the force a sample feels, while doubling the radius only doubles it — small increases in speed dominate the outcome, which is why centrifuges carry conservative maximum-speed ratings. This asymmetry is also why lab protocols are written in × g rather than in RPM: a benchtop microcentrifuge with a 7 cm rotor and a floor model with a 15 cm rotor spinning at the identical RPM subject a sample to very different forces, but a protocol stated in × g transfers cleanly between them, because both machines can be dialed to reach the same number.
The radius that belongs in the formula is the distance from the spin axis to the point in the tube where the pellet actually forms — usually rmax, the tube's farthest point from the axis, not the distance to the rotor's centre of mass. Rotor manufacturers publish rmax, and often rmin and ravg, precisely because the wrong one under- or overstates the force by the ratio of the radii. Swing-out rotors add a further wrinkle: the bucket pivots outward once spinning, so the radius that matters is the swung-out operating radius, not the shorter one measured with the rotor at rest.
- Enter the Rotor radius, cm — measured from the spin axis to the point in the tube where the sample sits at full speed (rmax), not to the rotor's centre.
- Enter the Rotor speed, RPM you intend to run, taken from the centrifuge dial or from the protocol's target speed.
- Read the Relative centrifugal force (×g) result — this is the ×g figure lab protocols actually specify.
- If a protocol states a target ×g instead of an RPM, try radius and RPM combinations until Relative centrifugal force (×g) matches the value the protocol calls for.
Worked example — a 10 cm rotor at 4,000 RPM
A benchtop microcentrifuge fitted with a fixed-angle rotor rated at rmax = 10 cm is set to spin at 4,000 RPM. Plugging straight into the formula: RCF = 1.118 × 10⁻⁵ × 10 × 4000² = 1.118 × 10⁻⁵ × 10 × 16,000,000 = 1,788.8. The sample experiences 1,788.8 × g — nearly 1,800 times its own weight — a routine setting for pelleting bacterial cells or precipitating nucleic acids on the bench.
A protocol calling for '1,800 × g for 10 minutes' translates directly onto this rotor at 4,000 RPM. Swap in a rotor with a smaller 6 cm radius and reaching that same 1,788.8 × g needs roughly 5,164 RPM instead, since RCF scales with the square of the RPM but only linearly with radius. That is exactly why bench protocols are written in × g rather than in machine-specific RPM — the figure describes the force the sample feels, not one instrument's dial setting.
Questions
Why does RPM alone not tell you the g-force a sample feels?
Because RCF depends on both speed and radius, and RPM only captures speed. A 10 cm rotor at 4,000 RPM produces 1,788.8 × g, but a 20 cm rotor at that same 4,000 RPM produces exactly double, 3,577.6 × g — identical speed, twice the radius, twice the force. Two centrifuges running the same RPM can expose samples to very different, sometimes damaging, forces if their rotors differ in size.
What radius should I actually enter for r?
Enter rmax — the distance from the spin axis to the point farthest from that axis where the sample settles, usually the bottom of the tube at full speed. Rotor manufacturers publish this figure on the spec sheet or stamp it on the rotor itself. Using the axis-to-rotor-centre distance instead, or a swing-out bucket's resting radius rather than its swung-out radius, understates the true force and can under-pellet a sample.
Why is the constant in the formula 1.118 × 10⁻⁵?
It folds three conversions into one number: RPM to radians per second (multiply by 2π/60, then square), centimetres to metres (divide by 100), and metres per second squared to multiples of gravity (divide by 9.80665). Multiplying those factors together — (2π/60)² ÷ 100 ÷ 9.80665 — gives 1.118 × 10⁻⁵, so the formula accepts rotor radius in centimetres and RPM straight off the dial with no manual unit conversion.
Is 1,788.8 × g a typical setting, or unusually high?
It sits mid-range for molecular biology bench work. Pelleting bacteria commonly calls for 3,000 to 5,000 × g, while plasmid miniprep and PCR cleanup spins often specify 10,000 to 20,000 × g. Ultracentrifuges separating cell organelles or viral particles reach 100,000 × g and beyond, using much smaller rotors spun far faster, because a small radius keeps the mechanical stress on the rotor survivable at the RPM required.
Does this formula work for ultracentrifuges too?
Yes — the physics is identical at any scale, since RCF is just centripetal acceleration expressed as a multiple of g. The practical limit is not the formula but the hardware: ultracentrifuge rotors are machined from titanium or carbon composite and run under vacuum specifically because an ordinary aluminium rotor would fail mechanically at the RPM needed to reach six-figure RCF on a small radius.
Does the sample's own mass change the RCF value?
No. RCF, like the g in weight, is an acceleration, not mass times acceleration. A 1 mg pellet and a 5 mL blood draw sitting at the same radius and RPM experience the identical 1,788.8 × g; only the mechanical stress the rotor and tube must withstand grows with the sample's mass, not the RCF figure itself.